Question

Ball position Ball Beam rotation Motor drive Beam Parameter Name m Mass of Ball Units kg Value 0.25 l Length of Rod m 2.0 R Radius of Ball m 0.1 $J_b$ Inertia of beam Nm/rad/s$^2$ 0.02 L Motor Inductance Henry 4.64 (10$^{-5}$) $R_m$ Motor Resistance Ohms 0.36 $J_m$ Inertia of Motor Nm/rad/s$^2$ 5.12 (10$^{-5}$) $K_b$ Motor Voltage Constant V/rad 0.014 $K_t$ Motor Torque Constant Nm/A 0.014 b Motor Torsional Damping Nm/rad/s 5.0

          Ball position
Ball
Beam rotation
Motor drive
Beam
Parameter
Name
m
Mass of Ball
Units
kg
Value
0.25
l
Length of Rod
m
2.0
R
Radius of Ball
m
0.1
$J_b$
Inertia of beam
Nm/rad/s$^2$
0.02
L
Motor Inductance
Henry
4.64 (10$^{-5}$)
$R_m$
Motor Resistance
Ohms
0.36
$J_m$
Inertia of Motor
Nm/rad/s$^2$
5.12 (10$^{-5}$)
$K_b$
Motor Voltage Constant
V/rad
0.014
$K_t$
Motor Torque Constant
Nm/A
0.014
b
Motor Torsional Damping
Nm/rad/s
5.0

Ball position
Ball
Beam rotation
Motor drive
Beam
Parameter
Name
m
Mass of Ball
Units
kg
Value
0.25
l
Length of Rod
m
2.0
R
Radius of Ball
m
0.1
Jb
Inertia of beam
Nm/rad/s^2
0.02
L
Motor Inductance
Henry
4.64 (10^-5)
Rm
Motor Resistance
Ohms
0.36
Jm
Inertia of Motor
Nm/rad/s^2
5.12 (10^-5)
Kb
Motor Voltage Constant
V/rad
0.014
Kt
Motor Torque Constant
Nm/A
0.014
b
Motor Torsional Damping
Nm/rad/s
5.0

Added by Meredith T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Anand Jangid

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a) Find the equation(s) of motion: Show more…

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a) Find the equation(s) of motion. b) Find the Transfer Function. c) Find the control Block Diagram. Ball position. Ball. Beam rotation. Beam. Motor drive. Parameters: - Mass of Ball. - Length of Rod. - Radius of Ball. - Inertia of Beam. - Motor Inductance. Units: - kg. - m. Values: - Mass of Ball: 0.25 kg. - Length of Rod: 1 m. - Radius of Ball: 0.02 m. - Inertia of Beam: 2.0 kg*m^2. - Motor Inductance: 0.1 Henry. - Motor Resistance: 4.64 (10^-2) Ohms. - Inertia of Motor: 0.36 Nm/rad/s^2. - Motor Voltage Constant: 5.12 (10^-5) V/rad. - Motor Torque Constant: 0.014 Nm/A. - Motor Torsional Damping: 0.014 Nm/rad/s.